on some properties of elements in hypergroup algebras

Let h be a hypergroup with left haar measure and let l^1 (h) be the complex lebesgue space associated with it. let l∞(h) be the set of all locally measurable functions that are bounded except on a locally null set, modulo functions that are zero locally a.e. let µ ∈ m(h). we want to find out when µf ∈ l∞(h)∗ implies that f ∈ l^1 (h). some necessary and sufficient conditions is found for a measure µ for which if µf ∈ l^1 (h) for every f ∈ l∞(h)∗, then f ∈ l^1 (h).